Comparison between different kriging estimators     

A. Boufassa  M. Armstrong 《Mathematical Geology》1989,21(3):331-345

Six different geostatistical estimators (linear kriging, lognormal kriging, and disjunctive kriging, each with and without a nonbias, i.e., universality condition) were compared using data from a polymetallic deposit in Algeria. The differences between estimators with and without the nonbias condition were far more pronounced than between the different kriging methods. This highlights the importance of choosing an appropriate stationarity model for the data. The criterion concerning kriging weight of the mean in simple kriging, proposed by Remacre (1984, 1987) and Rivoirard (1984) was found to be helpful for determining blocks where the choice of the stationarity hypothesis was critical.  相似文献   

Use of Geostatistics For Accurate Mapping of Earthquake Ground Motion     

James R. Carr  Charles E. Glass 《Geophysical Journal International》1989,97(1):31-40

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Random vectors and spatial analysis by geostatistics for geotechnical applications     

Dae S. Young 《Mathematical Geology》1987,19(6):467-479

Geostatistics is extended to the spatial analysis of vector variables by defining the estimation variance and vector variogram in terms of the magnitude of difference vectors. Many random variables in geotechnology are in vectorial terms rather than scalars, and its structural analysis requires those sample variable interpolations to construct and characterize structural models. A better local estimator will result in greater quality of input models; geostatistics can provide such estimators: kriging estimators. The efficiency of geostatistics for vector variables is demonstrated in a case study of rock joint orientations in geological formations. The positive cross-validation encourages application of geostatistics to spatial analysis of random vectors in geoscience as well as various geotechnical fields including optimum site characterization, rock mechanics for mining and civil structures, cavability analysis of block cavings, petroleum engineering, and hydrologic and hydraulic modelings.  相似文献   

Comparison of two techniques for applying disjunctive kriging: The Gaussian anamorphosis model versus the direct statistical inference of the bivariate distributions     

James R. Carr  Eddy D. Deng 《Mathematical Geology》1987,19(1):57-68

Indicator cokriging is an alternative to disjunctive kriging for estimation of spatial distributions. One way to determine which of these techniques is more accurate for estimation of spatial distributions is to apply each to a particular type of data. A procedure is developed for evaluation of disjunctive kriging and indicator cokriging for such an application. Application of this procedure to earthquake ground motion data found disjunctive kriging to be at least as accurate as indicator cokriging for estimation of spatial distributions of peak horizontal acceleration. Indicator cokriging was superior for all other types of earthquake ground motion data.  相似文献   

Trend-surface analysis     

G. S. Watson 《Mathematical Geology》1971,3(3):215-226

This paper is largely an exposition of the work of the French geostatistian G. Matheron and his school in English and at a simpler mathematical level. The probability theory on which it is based is essentially all contained in the references cited, most of which will be unfamiliar to mathematical geologists. The important method of universal kriging is explained intuitively. The genuine statistical problems, which have yet to be overcome, are pointed out.Research supported by the Office of Naval Research under contract NONR 4010(09) awarded to the Department of Statistics, The Johns Hopkins University. This paper in whole or in part may be reproduced for any purpose of the United States Government.  相似文献   

Geostatistical analysis of field hydraulic conductivity in compacted clay     

A. S. Rogowski  D. E. Simmons 《Mathematical Geology》1988,20(4):423-446

Hydraulic conductivity(K) of fractured or porous materials is associated intimately with water flow and chemical transport. Basic concepts imply uniform flux through a homogeneous cross-sectional area. If flow were to occur only through part of the area, actual rates could be considerably different. Because laboratory values ofK in compacted clays seldom agree with field estimates, questions arise as to what the true values ofK are and how they should be estimated. Hydraulic conductivity values were measured on a 10×25 m elevated bridge-like platform. A constant water level was maintained for 1 yr over a 0.3-m thick layer of compacted clay, and inflow and outflow rates were monitored using 10×25 grids of 0.3-m diameter infiltration rings and outflow drains subtending approximately 1×1 m blocks of compacted clay. Variography of inflow and outflow data established relationships between cores and blocks of clay, respectively. Because distributions of outflow rates were much less and bore little resemblance to the distributions of break-through rates based on tracer studies, presence of macropores and preferential flow through the macropores was suspected. Subsequently, probability kriging was applied to reevaluate distribution of flux rates and possible location of macropores. Sites exceeding a threshold outflow of 100×10^–9 m/s were classified as outliers and were assumed to probably contain a significant population of macropores. Different sampling schemes were examined. Variogram analysis of outflows with and without outliers suggested adequacy of sampling the site at 50 randomly chosen locations. Because of the potential contribution of macropores to pollutant transport and the practical necessity of extrapolating small plot values to larger areas, conditional simulations with and without outliers were carried out. Simulated scenarios based on all available data compared well with conditional simulations based on randomly chosen locations.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.  相似文献   

Kriging in terms of projections     

A. G. Journel 《Mathematical Geology》1977,9(6):563-586

In the last few years, an increasing number of practical studies using so-called kriging estimation procedures have been published. Various terms, such as universal kriging, lognormal kriging, ordinary kriging, etc., are used to define different estimation procedures, leaving a certain confusion about what kriging really is. The object of this paper is to show what is the common backbone of all these estimation procedures, thus justifying the common name of kriging procedures. The word kriging (in French krigeage) is a concise and convenient term to designate the classical procedure of selecting, within agiven class of possible estimators, the estimator with a minimum estimation variance (i.e., the estimator which leads to a minimum variance of the resulting estimation error). This estimation variance can be seen as a squared distance between the unknown value and its estimator; the process of minimization of this distance can then be seen as the projection of the unknown value onto the space within which the search for an estimator is carried out.  相似文献   

    

I. C. Lemmer 《Mathematical Geology》1986,18(7):589-604

For any distribution of grades, a particular cutoff grade is shown here to exist at which the indicator covariance is proportional to the grade covariance to a very high degree of accuracy. The name mononodal cutoff is chosen to denote this grade. Its importance for robust grade variography in the presence of a large coefficient of variation—typical of precious metals—derives from the fact that the mononodal indicator variogram is then linearly related to the grade variogram yet is immune to outlier data and is found to be particularly robust under data information reduction. Thus, it is an excellent substitute to model in lieu of a difficult grade variogram. A theoretical expression for the indicator covariance is given as a double series of orthogonal polynomials that have the grade density function as weight function. Leading terms of this series suggest that indicator and grade covariances are first-order proportional, with cutoff grade dependence being carried by the proportionality factor. Kriging equations associated with this indicator covariance lead to cutoff-free kriging weights that are identical to grade kriging weights. This circumstance simplifies indicator kriging used to estimate local point-grade histograms, while at the same time obviating order relations problems.This paper is based in part on a PhD thesis submitted to the Department of Applied Earth Sciences, Stanford University, Stanford, California 94305, in 1984 (unpublished).  相似文献   

    

Michael W. D. Davis  Michel David  Jean-Marc Belisle 《Mathematical Geology》1978,10(4):369-374

In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it is important that the program to solve the linear systems be as efficient as possible. Standard library routines tend to contain very general stable methods using pivoting and iteration to ensure high accuracy solutions. Here, a particular method has been developed that gives a substantial improvement in run time at the occasional expense of accuracy and stability. The method is not new—just a simple application of Gaussian elimination in the symmetric case.  相似文献   

A geostatistically based approach to the identification of aquifer transmissivities in Yolo Basin, California     

Mohamed Aboufirassi  Miguel A. Mariño 《Mathematical Geology》1984,16(2):125-137

A geostatistically based approach is developed for the identification of aquifer transmissivities in Yolo Basin, California. The approach combines weighted least-squares with universal kriging and cokriging techniques in an overall scheme that (1)considers a prioriknown information on aquifer transmissivity and specific capacities of wells, (2)considers uncertainties in water level and transmissivity data, and (3)estimates the reliability of the generated transmissivity values. Minimization of a global least-squares function that incorporates calibration and plausibility criteria leads to a transmissivity map that shows a good agreement with pumping-test results.  相似文献